derive centre of mass i e cm = m1r1 + m2r2 / m1+m2 - Physics - System Of Particles And Rotational Motion

Question

derive centre of mass i e cm = m1r1 +
m2r2 / m1+m2

Vara · Accepted Answer

Dear
Student,
Please find below the solution
to the asked query:
Consider two particles of masses m1 and m2 which are separated by a distance r
Letr1=Distance of centre of mass from first particlex1=Distance of the first particle from origin=rcm-r1r2=Distance of centre of mass from second particlex2=Distance of the second particle from origin=r2-rcmxcm=Distance of the centre of mass from originAlgebraic sum of moment of masses about centre of mass is equal to zero
m1x1=m2x2m1rcm-r1=m2r2-rcmm1rcm-m1r1=m2r2-m2rcmrcmm1+m2=m1r1+m2r2Hence,rcm=m1r1+m2r2m1+m2
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derive centre of mass i.e cm = m1r1 + m2r2 / m1+m2

derive centre of mass i.e cm = m₁r₁ + m₂r₂ / m₁+m₂